mkfun.tp {gss}R Documentation

Crafting Building Blocks for Thin-Plate Splines

Description

Craft numerical functions to be used by mkterm.tp to assemble model terms.

Usage

mkrk.tp(dm,order,mesh,weight)
mkphi.tp(dm,order,mesh,weight)

mkrk.tp.p(dm,order)
mkphi.tp.p(dm,order)

Arguments

dm Dimension of the variable d.
order Order of the differential operator m.
mesh Normalizing mesh.
weight Normalizing weights.

Details

Thin-plate splines are defined for 2m>d.

mkrk.tp.p generates the pseudo kernel, and mkphi.tp.p generates the (m+d-1)!/d!/(m-1)! lower order polynomials with total order less than m.

mkphi.tp generates normalized lower order polynomials orthonormal w.r.t. a norm specified by mesh and weight as described in the reference, and mkrk.tp conditions the pseudo kernel to generate the reproducing kernel orthogonal to the lower order polynomials w.r.t. the norm.

Value

A list of two components.

fun Function definition.
env Portable local constants derived from the arguments.

Note

mkrk.tp creates a bivariate function fun(x,y,env,outer=FALSE), where x, y are real arguments and local constants can be passed in through env.

mkphi.tp creates a collection of univariate functions fun(x,nu,env), where x is the argument and nu is the index.

References

Gu, C. and Wahba, G. (1993), Semiparametric analysis of variance with tensor product thin plate splines. Journal of the Royal Statistical Society Ser. B, 55, 353–368.

See Also

mkfun.poly, mkrk.factor.